What is the integral from 0 to infinity of 2/(x^2+4) ?

The integral from 0 to infinity of 2/(x^2+4) is pi/2

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integral from 0 to infinity of 2/(x^2+4)

\int_{0}^{\infty} \frac{2}{x ^{2} + 4} d x

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

\int_{0}^{\infty} \frac{2}{x ^{2} + 4} d x

Compute the indefinite integral:

\int \frac{2}{x ^{2} + 4} d x = arctan (\frac{x}{2}) + C

Compute the boundaries:

\int_{0}^{\infty} \frac{2}{x ^{2} + 4} d x = \frac{π}{2} - 0

= \frac{π}{2} - 0

Simplify

= \frac{π}{2}

(1 + x^{2}) \frac{d y}{d x} + 3 x y = 5 x

y^{2} \frac{d y}{d x} = 1

\int x arctan (20 x) d x

\frac{x}{x ^{2} - 2}

\int (3 x^{2} + 5) cos (7 x) d x

What is the integral from 0 to infinity of 2/(x^2+4) ?
The integral from 0 to infinity of 2/(x^2+4) is pi/2